The simplest Taylor approximation of a function f which has multiple parameters is:

(where H is the Hesse Matrix)

In Electrodynamics, functions of the following form appear for the electrostatic potential:

An example is:

How do we calculate the value of this function?

In order to find out, we develop the function into a Taylor Series with development point .

We now actually plug the function in:

So, what is ?

Hence,

Let . Then,

So, what is ?

Hence,

After plugging this into the original integral:

With:

Monopole momentum

Dipole momentum

Quadrupole momentum